The problem

1.

Consider the surface

$$z = 4-x^2-\frac{y^2}{4}.$$

If a ball rolls downward, starting at the point (1,0,3), where does it meet the z=0 plane? Using Maple, graph the surface and the path followed by the ball.

2.

For the same surface in problem 1, where does a ball starting at $\left(\frac{1}{4},1,\frac{59}{16}\right)$ meet the z=0 plane? Using Maple, graph the surface and the path followed by the ball.

3.

Suppose a ball is rolling down a saddle-shaped surface

z = x²-y².

If it starts at (3,1,8), where does it cross the z=0 plane? Using Maple, graph the surface and the path followed by the ball.